Properties of Neutrosophic Relator Spaces

Relator spaces provide a relational framework in which neighborhoods, interiors, closures, convergence and several topological properties can be generated directly from a family of binary relations. Independently, neutrosophic set theory extends classical and fuzzy descriptions by associating with every point three membership degrees representing truth, indeterminacy and falsity. In this paper we combine these two frameworks and develop a systematic theory of neutrosophic relator spaces. We define neutrosophic relator interiors and closures componentwise from a relator, and introduce neutrosophic open and closed sets, neutrosophic neighborhoods, induced neutrosophic topologies, continuity, separation properties, compactness and connectedness. Several basic algebraic and order properties of these operators are established. We show that the construction reduces to the corresponding theory of relator spaces when the three neutrosophic components are crisp, and to ordinary neutrosophic topological spaces when the relator is induced by a topology. Several examples are given, including finite relator spaces, symmetric relators, preorder relators and a crisp neutrosophic relator space. The resulting framework provides a common language for relational generalizations of neutrosophic topology and suggests further investigations involving convergence, quasiuniformity, bitopological structures and generalized separation axioms.